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10 days ago

#23

Mathematics

2 answers:

zzz [4K]10 days ago

0 0

The correct response is A.......

zzz [4K]10 days ago

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The correct response is C

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A straight rod has one end at the origin and the other end at the point (l,0) and a linear density given by λ=ax2, where a is a

Svet_ta [4296]

It is stated that a straight rod has one endpoint at the origin (0,0) and the opposite endpoint at (L,0), with a linear density defined by $\lambda=ax^2$ , where a is a constant and x is the x coordinate.

Thus, the infinitesimal mass is expressed as:

$dm=\lambda \times dx=\lambda dx$

The total mass can be calculated by integrating the above expression as follows:

$\int\,dm= \int\limits^L_0 {ax^2} \, dx$

Consequently, $m=a\int\limits^L_0 {x^2} \, dx=a[\frac{x^3}{3}]_{0}^{L}=\frac{a}{3}[L^3-0]= \frac{aL^3}{3}$

Now, we can calculate the center of mass, $x_{cm}$ of the rod as:

$x_{cm}=\frac{1}{m} \int xdm$

$x_{cm}=\frac{1}{m}\int_{0}^{L}x\times \lambda dx =\int_{0}^{L}x\times ax^2 dx=\int_{0}^{L}ax^3 dx$

Now, it follows that

x_{cm}=\frac{1}{\frac{aL^3}{3}}\int_{0}^{L}ax^3dx=\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}

Therefore, the center of mass, $x_{cm}$ is located at:

$\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}=\frac{3}{aL^3}\times \frac{aL^4}{4}=\frac{3}{4}L$

5 0

2 days ago

Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately.

Inessa [3895]

It’s straightforward, as you already have the slope and y-intercepts for each equation, enabling easy graphing.

I hope this is helpful <3

5 0

7 days ago

Read 2 more answers

Harper knows he is 50 yards from school. The map on his phone shows that the school is 34 inch from his current location. How fa

PIT_PIT [3895]

To solve this question, follow the steps outlined below:

1. Since 1 yard equals 36 inches, to convert 50 yards to inches involves:

$(50)(36)=1800in$

2. If he is standing 50 yards away from the school, and the map indicates that the school is 34 inches away from him, when it shows 3 inches the actual distance is:

$\frac{(1800in)(3in)}{34in}=158.82in$

3. If you express this back in yards:

$\frac{158.82}{36} =4.41 yd$

Consequently, the answer is: 158.82 inches or 4.41 yards.

8 0

8 days ago

Read 2 more answers

How many natural numbers are there between 8² and 9²

Svet_ta [4296]

Soccer game theory posits that the earliest participants in the game will play.

3 0

12 days ago

I JUST NEED THESE 3 QUESTIONS

AnnZ [3868]

Answer:

1. What are the amplitude and period of the sine function that indicates the positioning of the band members as they start performing?

Answer: The amplitude is 80 ft and the period is 60 ft.

2. Edna, seated in the stands, faces Darla and notices that the sine curve starts rising from the left edge of the field. What is the equation for the sine function representing the arrangement of band members at the beginning of their performance?

Answer: y = 80cos(x*π/30)+80

3. When the band starts playing, the members move away from the edges, and the sine curve changes to start decreasing at the far left. Darla remains in her position. Now the sine curve is half as tall as it originally was. What is the equation for the updated sine curve depicting the band members' positions?

Answer: y = 40cos(x*π/30)+80

4. Finally, the entire band shifts closer to the edge of the football field, causing the sine curve to now position itself in the lower half of the field from Edna’s perspective. What is the equation for this sine curve reflecting the band members' positions after these adjustments?

Answer: y = 40cos(x*π/30)+40

Step-by-step explanation:

8 0

5 days ago